Cheat mode:
Press Down, Down, Up, Up, Left, Right, Left, Right, 1, 2, Start at the title screen to enable cheat mode and a sound test option.

Level select:
Press Up, Up, Down, Down, Right, Left, Right, Left, Start at the title screen.

Quick emerald:
Press Up, Down, Up, Down, 1, 2, 1, 2, 1, 2 at the Sonic/Tails selection screen to automatically receive an emerald during level 1.

Fast run:
Press Up + 1 or Up + 2.

Fireballs:
Enable cheat mode. Press Down, Down/Right, Right, 1 during game play to shoot fireballs.